Computational Methods for Entry Length Heat Transfer by Combined Laminar Convection in Vertical Tubes

Abstract

Numerical techniques for the calculation of velocity and temperature distributions in heated ducts have proved accurate but expensive in computer time and capacity. It is worth investigating to what extent simplification is possible without loss of accuracy. Entry-length heat transfer to upward laminar flow with combined convection in a vertical tube is taken as typical. Comparison is made between measured values and, first, a full numerical solution for constant thermophysical properties (viscosity and thermal diffusivity), secondly, the same solution but allowing for their individual and combined variation with temperature and, thirdly, a solution which assumes a series of truncated versions of the fully developed temperature distribution to establish corresponding velocity profiles, allowing for temperature-dependent properties.

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